A new rotary MR damper applicable to a semi-active suspension system featuring a low level between road surface and floor

Abstract

This study presents a rotary magnetorheological (MR) damper for a suspension system of low floor vehicles (LFVs) where a large stroke cannot be achieved due to the space constraints of damper motion for special purposes. As is well known, MR dampers are highly suitable for the semi-active suspension systems, which show controllable damping force by an external magnetic field. One of the crucial geometrical parameters to achieve high damping force at the same magnetic field is the suspension stroke in conventional linear MR dampers developed or proposed so far. However, LFVs which include purpose-built vehicles (PBVs) and future smart mobilities, do not have enough space for the linear MR damper installation. Due to the confined space in LFVs, the shape of the MR damper and the magnetic circuit design need to be carefully devised to achieve the target damping force. In addition, the time delay of the MR damper which affects suspension performance should be considered in the modeling and control processing. In this work, the time delay caused by increased inductance is resolved using the Smith compensator, which is integrated into the control system to mitigate the time delay, ensuring effective real-time control. The target control range and operating angle were decided through mathematical modeling and simulation, followed by the prototype fabrication and the measurement of the field-dependent damping force characteristics of the rotary MR damper. Subsequently, a quarter-car suspension model with the proposed MR damper is established to evaluate the suspension performance of LVFs. It is shown from the control simulation that the ride comfort (ISO 2631) is enhanced by up to 21%, while the velocity response is reduced by up to 52% under smooth (ISO B-Class) and rough (ISO D-Class) road profiles, respectively. The results presented in this work are useful guidelines for future smart mobilities featuring the space confinement between floor and road for damper installation in the development of the semi-active MR suspension system.

Keywords

magnetorheological fluid rotary MR damper (RMRD)low floor vehicles (LFVs)in-wheel motor damping force semi-active suspension control dynamic model time delay compensation

Introduction

Magnetorheological (MR) dampers are widely utilized in semi-active suspension systems due to their tunable damping characteristics and rapid responsiveness to the change of the input current (or magnetic field). These properties make MR dampers ideal for enhancing ride comfort and vibration control in vehicles subjected to several different roads. For effective ride comfort and vibration control, the control range of the damping force must be both high and wide. However, achieving high damping forces typically requires larger damper sizes (length and inner cylinder radius) or increased coil turns, which pose challenges in low floor vehicles (LFVs) where constrained space limitations restrict damper size. To achieve the target damping force within the constrained space, increased coil turns are used, but this approach introduces significant inductance, resulting in slower time responses of MR damper (time delay) that hinder real-time suspension control.

Ride comfort is a critical dynamic performance characteristic ensured by the vehicle’s suspension system, which adjusts to absorb vibrations from road irregularities and accommodate driving conditions. Metrics such as the vertical velocity and acceleration of the sprung mass are frequently employed to evaluate ride comfort. Among these, vertical acceleration, as defined by ISO 2631-1, is considered the most significant for assessing the impact on passengers (ANSI/ASA S2.72-2002 (R2007) / ISO 2631-1:1997, 2002; Rimell and Mansfield, 2007; Tseng and Hrovat, 2015; Zhao and Schindler, 2014). To improve dynamic performance, many vehicles now employ Electronic Control Suspension (ECS) systems, which adjust damping characteristics using motors or hydraulic valves. However, ECS systems often face limitations, including complex structures, slow time response (high time delay), and discontinuous damping force (Ferhath and Kasi, 2024a, 2024b). To overcome these challenges, several works on the semi-active suspension systems utilizing MR fluid have been actively explored (Seong et al., 2011; Yao et al., 2002).

MR fluid, a smart material, can alter its apparent viscosity in real time under a magnetic field, enabling low time delays (fast response times), robustness against disturbances, and significant yield stress generation, making it ideal for vibration control applications including vehicle suspension system and flexible structures (Bitaraf et al., 2010; Cruze et al., 2018). In prior studies, Carlson et al. (1996) demonstrated the superiority of MR dampers with a skyhook controller, while Spencer et al. (1997) and Kamath et al. (1998) developed MR dampers with advanced models to address hysteresis and dynamic control. Despite these advancements, most studies focus on linear MR dampers, which inherently require longer dimensions due to the piston–cylinder structure and the necessary stroke length. Such dampers are therefore less suitable for low floor vehicles (LFVs), where available suspension installation space is limited in favor of maximizing passenger cabin space. LFVs, characterized by their low floor heights (e.g. 340 mm or less), necessitate compact suspension systems to ensure sufficient interior space.

This requirement aligns with the adoption of in-wheel motor technologies, which integrate powertrain and suspension components within the wheel. While in-wheel systems improve interior space and driving dynamics, they exacerbate space constraints for vertical linear dampers, limiting their applicability (Jin et al., 2021; Liu et al., 2017; Savitski et al., 2020; Xu et al., 2024).

To address these limitations, this paper proposes a novel rotary MR damper (RMRD) and control system specifically designed for low floor vehicles (LFVs), where suspension installation space is severely constrained. The RMRD is designed to optimize space utilization while retaining the inherent advantages of MR dampers. This development effort focuses on achieving the required damping range for LFVs within limited packaging constraints by optimizing the RMRD design accordingly. The anticipated cross-sectional view of the RMRD installation is shown in Figure 1. The design features a linkage structure with a lower arm to convert the torque generated by the RMRD into vertical damping force, ensuring sufficient force generation within the constrained space. However, only a few rotary MR dampers have been proposed so far. Giorgetti et al. (2010) identified advantages such as reduced fluid volume and low seal abrasion. However, this study lacked application-specific analysis for vehicles with constrained installation spaces, such as LFVs. Park et al. (2024) previously conducted a preliminary design of a rotary MR damper (RMRD) based on magnetic field and flow analyses. However, their study did not include experimental validation on a rotary actuator test bench, nor did it consider a controller or compensation for response delay. In this study, the performance and response delay of the RMRD were experimentally evaluated using a rotary-type excitation system, and the delay caused by the high inductance of the RMRD was compensated using a Smith Predictor-based control scheme. As a result, we propose a refined RMRD design suitable for low floor vehicles that address the installation angle and spatial limitations of conventional linear dampers due to stroke length, and we develop a delay-compensated control logic that enables fully controllable, high-performance operation.

The key contributions of this study are summarized as follows:

A novel rotary magnetorheological damper (RMRD) was designed and fabricated specifically for low floor vehicles (LFVs), that satisfy both high damping force requirements and strict spatial constraints. The study includes the configuration design, prototype fabrication, and experimental characterization of the damping performance of the proposed RMRD.

A dynamic model incorporating the Spencer model and current-dependent time delay was developed and experimentally validated.

A Smith predictor-based compensator was designed to mitigate response delay, enabling accurate force tracking under real-time conditions.

Comparative simulations against linear MR dampers confirmed the superiority of the proposed RMRD in terms of controllable force range.

Furthermore, a quarter-car suspension model equipped with the RMRD was simulated under two distinct road profiles, demonstrating up to 21% improvement in ride comfort compared to the uncontrolled case.

These findings highlight the feasibility and effectiveness of the proposed compact rotary MR damper as a next-generation semi-active suspension technology for LFVs, including purpose-built vehicles (PBVs) and other emerging mobility platforms.

Configuration and modeling

Configuration and operating principle

As outlined in the introduction, this study establishes initial targets or requirements for designing a rotary MR damper. The rotary damper for low floor vehicles (LFVs), which is the main focus of this study, is designed to reduce vehicle height while generating sufficient force for the effective control of LFVs.

To achieve this, a flow-type damper was adopted, which, although limited in operating range, can produce high damping force. The flow-type configuration is one of the operational modes of MR applications, where MR fluid flows through narrow channels to generate damping force. This method is widely used in MR dampers because it generates larger forces compared to other methods, such as shear mode.

The MR rotary damper developed in this study was also designed as a flow-type damper. Consequently, a stator was incorporated to restrict the rotational radius to ±30°. The target maximum damping torque for the rotary MR damper was determined by considering the range required for effective vibration control in LFVs. The specifications were set as follows: (i) A control range of less than 350 N under minimum current input (Soft Type) and over 2100 N under maximum current input (Hard Type), both measured at the maximum excitation speed of 30 rpm (approximately 0.5 m/s damper operating speed); (ii) An operating angle range for the vane of approximately ±30°. The overall configuration of the proposed MR rotary damper was presented in Figure 2, which was designed to meet the target specifications while accounting for the structural and mechanical constraints associated with application in LFVs.

The damper can be divided into four main components: the Stator (A), which generates electromagnetic force, the Shaft (B) connected to the external structure supporting the damper and serving as the axis of rotation, the Rotor (C) connected to the Shaft and responsible for generating fluid flow in the Magnetorheological Fluid (MRF), and the External housing (D) serving as a casing. First, the Stator marked as (A) in the diagram is a crucial component for forming the electromagnetic field in the MR damper. It consists of a solenoid coil-wound vane and a metal core to form magnetic flux lines. When current is applied, a magnetic field is formed along the core, allowing control of the damper’s damping force.

The Shaft marked as (B) is connected to external housing (D) and bearings to convert vertical motion caused by wheel vibration into rotational motion. The Rotor marked as (C) is connected to the Shaft via a key and is responsible for converting rotational motion induced by the connected vane into fluid flow in the MRF. It also forms a magnetic field along with the outer core. The gap between the Stator and Rotor serves as the orifice that induces damping force in the damper. Controlling the magnetic field in this region adjusts the apparent viscosity of the MRF, thus controlling the operation of the rotary MR damper. The housing marked as (D) maintains the damper’s structure, ensures shaft alignment via bearings and prevents internal oil leakage and external air ingress.

RMRD theoretical modeling

This structural configuration facilitates the generation of pressure drops proportionate to rotational speed and input current. Equations (1) and (2) (Khan et al., 2012; Spencer et al., 1998) describe the pressure drops resulting from the viscosity and yield stress of the MR fluid, respectively. In these equations, variables such as $Q$ (Total flow), $P_{vis}$ (MR fluid viscosity pressure drop), $P_{y}$ (MR fluid magnetic properties yield stress pressure drop), $Δ P$ (Total pressure drop), $η$ (Viscosity coefficient of MR fluid), $h$ (Orifice gap(between rotor and stator) size), $L$ (Length inside the core), $L_{p}$ (Magnetic pole length in the orifice gap), $w$ (Width of the damper), $D_{r}$ (Outer diameter of the MR core(Rotor)), and $D_{v}$ (Outer diameter of the vane rotor) are defined. Additionally, $τ_{y}$ represents the yield stress, $H$ represents the magnetic field intensity, ω denotes the angular velocity, $T$ signifies the static torque, and s(ω) represents the signum function concerning angular speed. equation (1) represents the pressure drop associated with flow-induced viscous effects, where the flow $Q$ occurs between the rotor and the housing. This pressure drop is proportional to the rotational speed. equation (2), on the other hand, accounts for the field-dependent pressure drop, which is influenced by the yield stress of the MR fluid and expressed as a function of the current input. Here, $c$ =2.07 + 1/(1 + 0.4T) within the interval (2.07, 3.07) (Kang et al., 2021). The total pressure drop, as per equation (3), combines contributions from rotational speed and input current. Pseudo-static rotational force, representing the static force or moment exerted on the rotating object, can be expressed in terms of torque using equation (4), utilizing the earlier obtained total pressure drop. equation (5) is the formula used to convert the rotational torque ( $T$ ) of the rotary damper into vertical force ( $F$ ), where $r$ represents the distance from the damper shaft to the wheel center (Moment Arm). The detailed derivation of equations (1)–(5) is provided in our previous study (Park et al., 2024).

P_{vis} = \frac{12 η L}{w h^{2}} (\frac{1}{h} - \frac{2 D_{r}}{{D_{v}}^{2} - {D_{r}}^{2}}) * Q

(1)

\begin{matrix} Q = \frac{{D_{v}}^{2} - {D_{r}}^{2}}{8} w * ω \\ P_{y} = c \frac{L_{p}}{h} | τ_{y} (H) | * sgn (ω) \end{matrix}

(2)

c = 2.07 + \frac{12 η | Q |}{12 η | Q | + 0.4 w h^{2} | τ_{y} (H) |}

(3)

\begin{matrix} Δ P = P_{vis} + P_{y} \\ T = \frac{{D_{v}}^{2} - {D_{r}}^{2}}{4} w * Δ P \end{matrix}

(4)

F = \frac{T}{r}

(5)

In this study, all references to the damping force represent the vertical force transmitted to the vehicle body, which is calculated by converting the torque generated by the rotary MR damper through the linkage mechanism composed of the upper and lower control arms. To maintain consistency and facilitate comparison with conventional linear MR dampers, this torque-to-force conversion is based on equation (5), where the moment arm ( $r$ ) is set to 150mm. The moment arm, which can be adjusted for different vehicle platforms, was selected to consider the linkage geometry of a commercial low floor vehicle (Figure 1). This conversion enables evaluation of the RMRD’s performance in terms of vertical force, which serves as the control variable in the quarter-car simulation model.

Figure 3 describes the variables included in equations (1)–(4) which shows the flow direction of the internal fluid according to the damper operation. The part indicated by the dotted green line is Stator(A) of Figure 2, and the part indicated by the dotted red line is Rotor(C) of Figure 2. The rotary MR damper was designed based on the target rotational angle of ±30°, as specified in Section 2.1. The internal parameters were initially modeled using equations (1)–(5), and detailed electromagnetic optimization is presented in Section 2.3.

Magnetic circuit optimization and parameter design

Electromagnetic analysis was performed using the Finite Element Method Magnetics (FEMM) software to validate the magnetic circuit design and determine key structural parameters of the RMRD. FEMM is specialized for 2D electromagnetic analysis and is widely utilized in academic studies due to its excellent compatibility with MATLAB (Desai et al., 2019; Yusoffa et al., 2021).

In this analysis, magnetic flux density (B) and magnetic field intensity (H) were evaluated under various current inputs (0.5, 1.0, and 1.5 A). Through iterative magnetic field simulations, essential design parameters of the RMRD such as the effective pole length and the number of coil turns were precisely determined to ensure the required magnetic field strength to achieve the target control range (Soft Type: ≤350 N, Hard Type: ≥2100 N). Figure 4(a) and (b) illustrate the generated magnetic flux density and magnetic field intensity distributions of the finalized optimal design parameters RMRD cross-section under the maximum current input (1.5 A).

In the figures, the regions depicted in red represent areas that have high magnetic flux density or magnetic field intensity. The simulation results show that the magnetic flux density was concentrated in the stator, rotor, and orifice gap, while the magnetic field intensity is particularly strong in the effective pole region (Lp1,2,3(as shown in Figure 3(b))) of the stator. These findings confirmed that the RMRD operated as intended, exhibiting ideal electromagnetic behavior for an MR damper. Based on these results, the dimensions of the stator and rotor were adjusted to ensure appropriate magnetic saturation within the core, thereby enabling optimal magnetic field application.

This electromagnetic control is the fundamental operating principle of the MR damper, enabling the control of damping torque by directly regulating the viscosity and yield stress of the MR fluid.

Table 1 summarizes the average magnetic field intensity (Avg.H) values within the effective pole region for each input current.

Table 1.

Average magnetic field intensity at Lp region under various currents.

Current	Lp1	Lp2	Lp3
0.5 A	22,137 A/m	21,463 A/m	22,160 A/m
1.0 A	46,395 A/m	46,641 A/m	46,446 A/m
1.5 A	70,987 A/m	73,078 A/m	71,034 A/m

These values were then used to estimate the expected damping torque using equations (1)–(5), which in turn guided the selection of the damper’s optimal geometry and materials.

The main structural parameters and materials used in the RMRD are listed in Table 2.

Table 2.

Geometric and material properties of the RMRD.

Parameter	Value
Damper(housing) diameter, $D$	0.164 m
Damper(housing) width, $w$	0.082 m
MR core(rotor) diameter, $D_{r}$	0.0791 m
Coil wire diameter	0.00075 m
Number of coil turns	110 turns
Core(rotor, stator) material	Steel 1008
Housing material	Steel 4340
Shaft material	Steel 4340
MR fluid	Lord Corp. 132 DG

For additional details regarding the fluid dynamics analysis and 3D-based electromagnetic simulation of the RMRD, please refer to our previous work (Park et al., 2024) and patent (Sohn et al., 2023).

Figure 5 presents the results of MATLAB simulations, which were implemented using the mathematical equations (1)–(5) described in Section 2.2, incorporating the structural parameters (Table 2) of the RMRD determined through the electromagnetic analysis in Section 2.3. In this test, discrete results were obtained at specific rotational speeds (RPM) to clearly represent the data points. The rotational speeds (RPM) were then converted into linear piston velocity (m/s) using equation (6), allowing for the construction of a force–velocity graph.

The figure illustrates the simulated force–piston velocity (F-V) characteristics, where the upper region of the graph corresponds to compression and the lower region corresponds to extension, showing the responses in both the compression and extension directions under maximum current input (Hard Type) and minimum current input (Soft Type) conditions. The simulation results confirmed that the target maximum force of 2100 N could be achieved at the maximum current input. Furthermore, the target damping force of less than 350 N under minimum current input was also achieved, leading to the development of a prototype for experimental validation.

piston velocity = 2 π \cdot (\frac{RPM}{60}) \cdot r

(6)

Prototype fabrication and test

Prototype fabrication

The prototype of the proposed rotary-type MR damper was fabricated as shown in Figure 6. The prototype was manufactured with an error margin of less than 0.001 mm from the design, which is within the acceptable tolerance level and suitable for application in the suspension system of LFVs. The experimental setup for measuring the maximum rotational damping force and time delay of the prototype is shown in Figure 7. The prototype was mounted on a rotary actuator capable of applying constant torque, and the rotational damping force was measured using a torque sensor (sensor model: HITEC_01166), while the rotational displacement was measured using an angle sensor (sensor model: TRANS-TEK_0603-0000-S-010101). A power supply (model: GW INSTEK_GPS-4303) was used to apply current, and all sensor data were collected using a DAQ system (model: NI_USB 6341).

Before the experiment, preliminary excitation was conducted to adequately stir the fluid in the MR damper, and additional preliminary excitation was performed before each subsequent test after the completion of the previous one. The excitation conditions for evaluating the damper’s performance were set at 1, 2, 3, 4, 6, 8, 10, 15, 20, 25, and 30 rpm. The damper was tested in both the clockwise (+30°) and counterclockwise (−30°) directions at 0, 0.5, 1.0, and 1.5 A.

Damping force results

The measured force-piston velocity (F-V) damping curve is presented in Figure 8, with the torque measurements obtained using the torque sensor converted to force. The solid lines represent the results obtained from the experiments, while the dotted lines indicate the results derived from MATLAB simulations. The experimental results showed slight discrepancies compared to the simulation, with most of the measured performance outcomes being higher than the simulation results. Specifically, under the 1.0 A and 30 rpm (0.5 m/s) conditions, the error rate was 3.25%, indicating a very high level of agreement between the simulation and experimental results. However, under the 1.5 A and 30 rpm conditions, the error rate increased to 13.56%, with the experimental results exceeding the simulation predictions.

This is presumed to be due to the influence of internal friction within the damper during the actual experiment, whereas the simulation results did not account for friction, leading to the observed differences. Additionally, under more severe operating conditions, such as higher current and faster speeds, it was observed that factors like friction, which are challenging to account for in simulations, became more prominent. It has been noted from the damping force characteristics that the proposed RMRD meet the performance target of controllable range exceeding 2100 N at maximum and below 350 N at minimum at 30 rpm (0.5 m/s), justifying one of the primary objectives (technical contributions). Therefore, the design objective of this study to develop a rotary MR damper with the targeted control range with a rotational angle of 30° has been successfully achieved.

To verify the effectiveness of the rotary MR damper in the confined space, a small linear damper with specifications suitable for LFVs was selected as a comparison target. The selection was based on the suspension installation space, defined as the space between the upper arm and lower arm shown in Figure 1. The damper’s stroke length was set to ±50 mm, and the piston height (Length of Orifice) was designed to be 24% of the vehicle suspension’s installation space, considering the housing thickness and gas chamber space within the suspension installation area. Accordingly, the small linear MR damper was designed with reference to a previous study (Sohn et al., 2015), and its key design parameters are summarized in Table 3. Based on these parameters, the damping force performance was evaluated under the same excitation conditions as RMRD. Damping force performance tests were conducted at different current levels (0.0, 0.5, 1.0, and 1.5 A), and the experimental results are presented in Figure 9(a) and (b). Figure 9(a) shows the force–displacement characteristics, while Figure 9(b) shows the force–velocity characteristics. The linear MR damper was observed to generate a maximum vertical damping force of 1895 N at 1.5 A. However, this value is lower than the RMRD shown in Figure 8.

Table 3.

Design parameters of linear MR damper.

Parameter	Value
Length of orifice	0.024 m
Diameter of piston	0.0534 m
Diameter of rod	0.01 m
Gap size of orifice	0.00085 m
Effective pole length	0.0012 m

More specifically, as shown in Figure 5, the linear MR damper fails to meet the target controllable range (soft type: ≤350 N, hard type: ≥2100 N) required for small low floor vehicles, as also discussed in Section 2. In order to adapt the linear damper for LFV application, its physical size had to be significantly reduced. However, this downsizing led to an insufficient damping force range. To achieve the required force range with a linear damper, its size must be increased accordingly. However, this is impractical for low floor vehicles due to the severely constrained suspension installation space, as it may necessitate compromising the available interior cabin space for passengers.

In contrast, the rotary MR damper developed in this study was able to provide the target controllable range even within the limited space. Therefore, the proposed rotary MR damper secured both practicality and feasibility, demonstrating its suitability for effective vibration control in LFVs, where suspension installation space is severely constrained. The results obtained in this work ensure that new types (or shapes) of MR dampers are required for the successful application of the semi-active suspension systems of future vehicles, including in-wheel motor electrical vehicles, one-pivot rotational vehicles, sliding motion vehicles, and so forth, which are featured by LFVs.

Time delay measurement

One of the key characteristics of MR fluid is its fast and reversible response, making it suitable for various dynamic systems exposed to relatively high-frequency disturbances. For effective vehicle control, the time delay of the suspension system must be fast; if the system has a significant time delay, the control effectiveness may decrease or even deteriorate. The condition for measuring the time delay of the RMRD involved performing triangular wave excitation at a constant speed of 1 rpm (0.015 m/s) to ensure low-speed excitation at a uniform rate and applying a current of 0.5, 1.0, 1.5 A at the same angular timing. The time delay was calculated based on the time difference between the current application and when the damper’s performance reached 63.2% of its maximum (Figure 10; Lee and Choi, 2019). This was measured three times in the clockwise direction, and the average value was used for the control system. The results of three repeated measurements for each current input are summarized in Table 4. The measured results may exhibit slight deviations due to the experimental environment.

Table 4.

Time delay results at 1 rpm.

Trial	Time delay
	0.5 A	1.0 A	1.5 A
First	63 ms	90 ms	120 ms
Second	70 ms	86 ms	118 ms
Third	82 ms	104 ms	147 ms
Average	72 ms	93 ms	128 ms

The variation in time delay observed across different current levels is presumed to be caused by limitations in the output capacity of the power supply and thermal effects during high-current operation, which may lead to changes in the internal electromagnetic characteristics of the damper. These assumptions will be validated through future research.

In this study, the time delay of the rotary MR damper was analyzed by averaging the measured time delays at various current inputs. The result showed a delay of 97.7 ms, which is slower than the typical time delay of conventional linear MR dampers (approximately 50 ms).

This is attributed to the structural characteristics of the rotary MR damper, which require a longer coil length compared to conventional linear MR dampers, resulting in increased inductance. To address the slower time response (high time delay) caused by increased inductance in the rotary MR damper, a Smith Predictive Compensator was designed and implemented (Velagic, 2008). The Smith Predictive Compensator for the time delay accurately predicts the system’s response and adjusts the control input accordingly. This approach ensures that the damper’s performance aligns with real-time suspension system requirements, even under significant delays.

Control of suspension system for LFVs

A quarter-car model with RMRD

A two-degree of freedom (2-DOF) quarter-car suspension model was used to evaluate the control performance of the proposed rotary magnetorheological damper (RMRD) for low floor vehicles (LFVs). This model structure is commonly used for suspension dynamics analysis that maintains a balance between simplicity and accuracy by including the importance of vertical dynamics (Kim et al., 2024; Shehata Gad et al., 2019).

As illustrated in Figure 11, the system consists of a sprung mass ( $m_{s}$ ) and an unsprung mass ( $m_{u}$ ), interconnected via a spring and damper in parallel with the actuator. The unsprung mass includes wheel-related components such as tires, brake systems, and hub structures, while the sprung mass accounts for the vehicle body, cabin structure, and payload. In conventional vehicles, the unsprung mass is approximately 40 kg; However, this value significantly increases in LFVs with in-wheel motors due to the integration of additional mechanical assemblies such as stators, rotors, and steering linkages.

Vertical displacements of the sprung and unsprung masses are denoted as $Z_{s}$ and $Z_{u}$ , respectively. The actuator, modeled as the RMRD, is integrated in parallel with the spring and damper elements. Road input profiles are represented by $Z_{r}$ . During the initial controller design, the damper is approximated as a linear element with constant damping coefficient ( $c_{s}$ ), suspension stiffness ( $k_{s}$ ), and tire stiffness ( $k_{t}$ ).

\begin{matrix} x = [Z_{s} {\overset{\cdot}{Z}}_{s} Z_{u} {\overset{\cdot}{Z}}_{u}]^{T} \\ \overset{\cdot}{x} = A x + B u + L Z_{r} \end{matrix}

(7)

A = [\begin{matrix} 0 & 1 & 0 & 0 \\ - k_{s} / m_{s} & c_{s} / m_{s} & k_{s} / m_{s} & c_{s} / m_{s} \\ 0 & 0 & 0 & 1 \\ - k_{s} / m_{u} & c_{s} / m_{u} & - (k_{s} + k_{t}) / m_{u} & - c_{s} / m_{u} \end{matrix}]

B = {[\begin{matrix} 0 & 1 / m_{s} & 0 & - 1 / m_{u} \end{matrix}]}^{T}

L = {[\begin{matrix} 0 & 0 & 0 & k_{t} / m_{u} \end{matrix}]}^{T}

From the free-body diagrams in Figure 11, the governing equations of motion are derived and used to construct the state-space representation, as shown in equation (7).

The parameters used in the simulation are listed in Table 5. While most parameters were adapted from a small passenger vehicle dataset in IPG CarMaker software (Büyükköprü et al., 2021; Ricciardi et al., 2019), the unsprung mass was modified to 100.908 kg to reflect the in-wheel motor configuration.

Table 5.

Parameter values of the 2-DOF quarter-car.

Parameter	Description	Value
$m_{s}$	Sprung mass	451 kg
$m_{u}$	Unsprung mass	100.908 kg
$k_{s}$	Spring stiffness	25,000 N/m
$c_{s}$	Damping coefficient	100 N*s/m
$k_{t}$	Tire stiffness	300,190 N/m

A schematic of the complete control system is presented in Figure 12. In this architecture, the desired force computed by the controller is converted into a current command via an inverse model, which is then applied to the MR rotary damper. However, due to the inherent time delay in the actuator, a discrepancy arises between the desired(target) and actual forces. To resolve this issue, a current-dependent time delay compensation system was developed using a Smith Predictive Compensator, based on the dynamic model and inverse model, ensuring that the desired force calculated by the controller is accurately compensated and implemented. This compensation mechanism improves performance by mitigating delay-induced errors in the MR damper.

Dynamic and inverse dynamic model

A modified Bouc-Wen model(Spencer model) originally proposed by Spencer et al. (1997) to accurately model the nonlinear and hysteretic behavior of the rotary magnetorheological damper (RMRD) was adopted in this study. The Spencer model is capable of modeling the force of MR damper based on displacement data, velocity data, and applied current values. It is known to accurately predict the behavior of MR dampers under a wide range of inputs.

The model consists of a parallel configuration of a linear spring–damper element and a nonlinear hysteretic component, as illustrated in Figure 13.

The total damping force ( $F$ ) of the MR damper is expressed as:

F = c_{1} \overset{\cdot}{y}

(8)

where $\overset{\cdot}{y}$ represents the velocity of the parallel system composed of the linear and hysteretic elements. The internal dynamics of the linear spring–damper subsystem are governed by:

\overset{\cdot}{y} = \frac{1}{c_{0} + c_{1}} [c_{0} \overset{\cdot}{x} + k_{0} x + α z]

(9)

Here, x is the relative displacement across the damper, $\overset{\cdot}{x}$ is the corresponding velocity, z is the internal hysteretic variable, and α, $c_{0}$ , $c_{1}$ , and $k_{0}$ are model parameters representing the hysteresis scale, viscous damping coefficients at high and low velocities, and linear stiffness, respectively. The evolution of the hysteretic variable z, which captures the nonlinear rate-dependent and memory behavior of the MR damper, is defined as:

\overset{\cdot}{z} = - γ | \overset{\cdot}{x} - \overset{\cdot}{y} | z | z |^{n - 1} - β (\overset{\cdot}{x} - \overset{\cdot}{y}) {| z |}^{n} + A (\overset{\cdot}{x} - \overset{\cdot}{y})

(10)

where β, γ, n, and A are dimensionless parameters controlling the shape and smoothness of the hysteresis loop.

To capture the current-dependent behavior of the MR fluid, the parameters α, $c_{0}$ , and $c_{1}$ are expressed as functions of the input current (t−τ), considering the inductive time delay τ inherent in the electromagnetic circuit:

α = α_{a} + α_{b} I (t - τ)

(11)

c_{0} = c_{0 a} + c_{0 b} I (t - τ)

(12)

c_{1} = c_{1 a} + c_{1 b} I (t - τ)

(13)

In these expressions, $c_{0 a}$ and $c_{1 a}$ represent the viscous damping components in the absence of current input, while $c_{0 b}$ and $c_{1 b}$ account for the variation in viscous damping induced by the application of current to the MR fluid.

This approach enables the model to capture both the amplitude scaling and response delay effects introduced by magnetic field variation and coil inductance. The model parameters were experimentally identified through curve fitting of measured force–velocity responses under various current and excitation conditions. A summary of the final identified parameter values is presented in Table 6.

Table 6.

Parameter values of the spencer model in 1.5 A.

Parameter	Value	Parameter	Value
$k_{0}$	0.0067 N/m	$c_{1 a}$	875 N*s/m
$c_{0 a}$	439 N*s/m	$c_{1 b}$	3389 N*s/m A
$c_{0 b}$	666 N*s/m A	$β$	6000.2861 m⁻²
$α_{a}$	94.4723 N/m	$γ$	0.0010 m⁻²
$α_{b}$	1698.7358 N/m A	$n$	14.9454
A	126.0006

This modeling framework has been widely used in MR damper studies and is known to provide high accuracy in capturing the complex dynamics of smart damping devices (Liu et al., 2011; Yun et al., 2010).

The predicted response of the MR rotary damper, calculated using the parameters derived for the Spencer model, is shown in Figure 14. In the figure, the solid line represents the results measured through actual experiments, while the dashed line indicates the predictions of the Spencer dynamic model for each applied current. The predicted model closely matches the actual damper response measured during performance tests at applied currents of 0.0, 0.5, 1.0, and 1.5 A, confirming the validity and accuracy of the developed Spencer model.

In the control system for the MR damper, both the control force and the command current must be computed. The flowchart for controlling the MR damper is included in Figure 12. The control force is dynamically calculated using the Spencer model, which requires the input current (I) to modulate the damping force by altering the rheological properties of the MR fluid via the applied magnetic field. Therefore, an inverse model is required to translate the desired damping force that is computed by the controller into the appropriate command current (I), which is then applied to the forward model (Spencer dynamic model) to generate the actual damping force in real-time. The use of an inverse model is essential to enable effective control of MR dampers. Therefore, a previous study has investigated various methods for implementing such inverse models (Tsang et al., 2006). In this study, the inverse model was implemented using a lookup-table based interpolation approach in a MATLAB Function block within the Simulink environment. As shown in Figure 15, the model first establishes a predicted force range generated from the forward MR damper model (Spencer dynamic model) at discrete current levels (0.0, 0.5, 1.0, and 1.5 A). When a desired force (calculated by the controller) is given, the inverse model searches the predicted force table to identify the two adjacent current levels between which the target force lies. Then, it uses linear interpolation to compute the precise current required to produce the desired damping force. This approach allows for real-time and continuous estimation of the command current while ensuring that the commanded force stays within the feasible operational range of the MR damper. Moreover, the model is computationally efficient and suitable for real-time embedded control applications.

Time delay compensator

To mitigate the impact of time delay, this paper applies the Smith predictive compensation control method (Zhang and Chen, 2024), with its schematic shown in Figure 16. In this figure, $G_{c} (s)$ represents the transfer function of the controller, while $G_{p} (s)$ and ${\hat{G}}_{p} (s)$ represent the actual and estimated transfer functions of the controlled system, respectively, and τ denotes the time delay. The transfer functions for the closed-loop system with and without the Smith predictive compensation model are expressed in equations (14) and (15).

\frac{Y (s)}{R (s)} = \frac{G_{c} (s) G_{p} (s)}{1 + G_{c} (s) G_{p} (s) e^{- τ s}}

(14)

\frac{Y (s)}{R (s)} = \frac{G_{c} (s) G_{p} (s) e^{- τ s}}{1 + G_{c} (s) {\hat{G}}_{p} (s) + G_{c} (s) e^{- τ s} (G_{p} (s) - {\hat{G}}_{p} (s))}

(15)

It can be observed that after the Smith predictive compensation model is applied, the denominator of the transfer function will no longer include $e^{- τ s}$ if both the estimated transfer function of the system and the estimated time delay are accurate ( ${\hat{G}}_{p} (s) \approx G_{p} (s)$ ), indicating that the effect of the time delay has been decreased.

In this study, both ${\hat{G}}_{p} (s)$ and $G_{p} (s)$ were constructed using the Spencer model of the MR damper, and the time delay was divided separately to reflect the characteristics of the MR damper that vary depending on the applied current.

In Section 4.1, the internal operating structure and principle illustrated as the Controller & Compensator in Figure 12 correspond to the Smith Predictive Compensation Control, which is highlighted by the red dashed line in Figure 16. Additionally, the section highlighted by the blue dashed line in Figure 16 corresponds to the Actuator (RMRD) and Vehicle Model (In-Wheel Motor LFVs) depicted in Figure 12.

The desired force calculated through the Smith Predictive Compensation Control is implemented via the MR Damper (Actuator) to control the ride comfort of the LFVs. Additionally, the controller represented as $G_{c} (s)$ in Figure 16 employs the skyhook controller, which has been extensively studied for ride comfort control (Farah et al., 2024; Leblebici and Türkay, 2018; Yi and Song, 1999).

The skyhook controller performs control using the damping force ( $c_{sky}$ ) associated with the absolute velocity of the sprung mass ( $\overset{\cdot}{x}$ ). The control equation for the skyhook control is shown in equation (16), and further details can be found in (Leblebici and Türkay, 2018).

F_{sky} = - c_{sky} \cdot \overset{\cdot}{x}

(16)

Results and discussions

The dynamic model, inverse model, and the Smith compensator for time delay compensation of the developed MR rotary damper were designed and analyzed using MATLAB and Simulink. The input road profiles for result evaluation were generated based on the international standard ISO 8608 (Technical Committee, 1995) and include a B-Class Road and a D-Class Road. According to ISO 8608, road profiles are categorized into different classes based on their Power Spectral Density (PSD) of elevation irregularities. The B-Class Road represents a relatively low level of surface roughness, with PSD values typically ranging between 10⁻⁶ and 10⁻⁵m²/rad, classifying it as a smooth road condition according to the international standard. On the other hand, the D-Class Road represents a higher level of surface roughness, with PSD values typically between 10⁻⁴ and 10⁻³ m²/rad, characterizing it as a rough road condition. Both road profiles were set to simulate driving at a fixed vehicle speed of 50 km/h, allowing for verification of results on both smooth and rough roads. The input road profiles are illustrated in Figure 17(a) and (b). Figure 17(a) and (b) represent B-Class and D-Class Road profiles, respectively, as defined by ISO 8608. The simulation evaluation was conducted by applying these road profiles to a quarter-car model and analyzing the resulting motion of the vehicle body(sprung mass).

Figure 18(a), (b), (c), and (d) present the results of the inputs applied to Figure 17(a) and (b) road profiles under three conditions to evaluate the performance degradation caused by damper time delay and the effectiveness of the time delay compensator. The three conditions are: without control (W/O), the Skyhook controller with damper delay (SH with Delay), and the controller with time delay compensation (SH with Smith). Figure 18(a) and (b) show the displacement and velocity responses of the sprung mass, respectively, when the B-Class Road profile (Figure 17(a)) is applied to the quarter-car model. Similarly, Figure 18(c) and (d) illustrate the displacement and velocity results under the D-Class Road profile (Figure 17(b)).

The acceleration result graph of the sprung mass was omitted due to space limitations. However, the quantitative results presented in Table 7 include ISO 2631 ride comfort indices, which are calculated based on sprung mass acceleration and allow for valid comparison.

Table 7.

Numerical control results.

Control Method	ISO 2631(Ride comfort; unit: - )		SP_Vel. RMS(unit: m/s)
	B-class	D-class	B-class	D-class
W/O	0.2464	1.1849	0.0287	0.1740
SH with Delay	0.2138	0.9430	0.0204	0.0884
SH with Smith	0.2133	0.9401	0.0201	0.0827

For clearer performance comparison among control scenarios, each graph includes a magnified section highlighting the interval where the differences are clearly shown. Control conditions are distinguished by color, as indicated in the legend, and results closer to zero are considered superior.

In both B-Class and D-Class Road conditions, the uncontrolled case (W/O) exhibited the largest displacement and velocity magnitudes, indicating the poorest performance. The “SH with Delay” case showed moderate improvement due to the skyhook controller, yet it was limited by the intrinsic time delay of the damper. In contrast, the “SH with Smith” condition, incorporating time delay compensation through a Smith predictive compensator, demonstrated improved displacement and velocity performance in most cases.

These observations are further supported by the RMS values obtained under each condition. For displacement, the SH with Delay condition showed improvements of 18.18% and 35.09% over the W/O condition on B-Class and D-Class roads, respectively, while the SH with Smith condition showed improvements of 18.08% and 36.40%, respectively.

For velocity, the SH with Delay condition demonstrated improvements of 28.92% and 49.20% over the W/O condition on B-Class and D-Class roads, respectively, while the SH with Smith condition achieved improvements of 29.97% and 52.47%, respectively. These results confirm the intended operation and effective implementation of both the skyhook controller and the Smith predictor to compensate for the time delay of the MR damper.

The improvement (IMP) is calculated using the following equation:

IMP = 100 - (\frac{Controlled Result}{Uncontrolled Result} \times 100)

(17)

This formulation enables objective comparisons between different control scenarios and clearly shows the effect of time delay compensation.

Figure 19(a) and (b) show the final current input to be applied to the MR damper, calculated through the control system with the time delay compensated controller (SH with Smith) for the B-Class random road (a) and the D-Class random road (b).

Appropriate current values were calculated based on the response of the vehicle model, and it was confirmed that the developed control system was designed to ensure the input current does not exceed the maximum value of 1.5 A for the rotary MR damper developed in this study.

In this study, SP_Vel RMS is used in conjunction with the ISO 2631 ride comfort index to comprehensively assess the effectiveness of the proposed rotary MR damper and its associated control system under various road conditions. SP_Vel RMS refers to the Root Mean Square of the vertical velocity of the vehicle body measured during driving. It is expressed in meters per second (m/s) and serves as a quantitative metric for ride comfort. Furthermore, since the Skyhook controller employed in this control system operates based on the velocity of the sprung mass, the SP_Vel RMS can be used to quantitatively compare the control performance and ride comfort outcomes. A lower SP_Vel RMS value indicates reduced vibration energy transmitted to the occupants, thereby implying improved ride comfort.

Another widely used index is ISO 2631 ride comfort standard (specifically the Wk-weighted RMS acceleration), that can evaluate whole-body vibrations typically experienced by seated passengers in vehicles. This metric emphasizes human sensitivity to vertical vibrations, especially in the 4–8 Hz frequency range known to cause the most discomfort. Although it is dimensionless, a lower ISO 2631 index value indicates better ride comfort performance. The numerical results are summarized in Table 7, where smaller values indicate better performance.

The ride comfort index in Table 7 is calculated as follows:

Ride Comfort = \sqrt{\frac{1}{T} \int_{0}^{T} a_{weighted}^{2} (t) dt}

(18)

In equation (18), T represents the total duration of the measurement or simulation, and $a_{weighted}$ (t) denotes the vertical acceleration filtered using the Wk-weighting standard defined in ISO 2631-1, which emphasizes the frequency range of 4–8 Hz known for high human sensitivity to vibration (Zhao and Schindler, 2014).

The ride comfort results based on ISO 2631 showed improvements of 13.23% for SH with Delay and 13.43% for SH with Smith compared to W/O on the B-Class random road. On the D-Class random road, SH with Delay showed an improvement of 20.42%, and SH with Smith showed an improvement of 20.66% compared to W/O, clearly demonstrating excellent vibration control performance overall. Additionally, the RMS results of the sprung mass velocity, used to verify the effectiveness of the control system, also showed significant improvements. On the B-Class random road, SH with Delay improved by 28.92%, and SH with Smith improved by 29.97% compared to W/O. On the D-Class random road, SH with Delay improved by 49.20%, and SH with Smith improved by 52.47% compared to W/O.

These results confirm that the control system leveraging the performance of the rotary MR damper developed in this study provides superior ride comfort control performance on both smooth and rough roads.

Conclusion

In this study, the design, development, and experimental validation of a rotary MR damper (RMRD) for application in future mobilities featuring LFVs were carried out and its effectiveness was validated by the semi-active quarter-car suspension model showing the improvement of the ride comfort under smooth and rough road profiles. The main technical points of this work include the design of a new RMRD to meet the required damping force of LVFs, the development of dynamic and inverse models, and the design of a control system to compensate for the time delay of MR damper. It has been demonstrated that the proposed RMRD generates a wider controllable damping force range than the conventional compact linear MR damper. As for the dynamic model, the Spencer model was adopted, and the time delay compensation was resolved using the Smith compensator.

The designed control system was evaluated under smooth road conditions (B-Class) and rough road conditions (D-Class), demonstrating excellent vibration and ride comfort control performance. The key results were analyzed using the ISO 2631 ride comfort index and RMS velocity outcomes. Significant improvements were observed, including 21% enhancement in the ride comfort index and 52% improvement in velocity response on D-Class Roads. These findings confirm the robust design of the ride comfort control system for LFVs with the proposed RMRD and demonstrate the effectiveness of the compensation system in mitigating the slower response time caused by the structural characteristics and control range of the rotary damper.

As mentioned in the Introduction, the distance between the road surface and the low floor of the car becomes increasingly smaller in future vehicles for specific purposes. Therefore, as one of the solutions to the space limitation for the suspension installation, a new rotary MR damper capable of achieving high damping forces within the constrained installation space of LFVs can be a potential candidate. In addition, the inevitable time delay of the MR damper caused by increased coil inductance has been successfully solved through the application of the Smith Predictor which is integrated with an enhanced real-time control scheme.

The results presented in this work confirm that the proposed rotary MR damper with an appropriate compensator associated with a suitable controller can provide robust solutions for enhanced suspension systems of future mobilities featured by low floor vehicles. It is finally remarked that the quarter-vehicle installed with the proposed RMRD is currently preparing for experimental tests under various road profiles with different controllers. Additionally, to verify the practical feasibility and replacement potential of the RMRD, a direct quantitative comparison with a linear damper is planned as future work, to be conducted on a test bench that replicates the actual linkage configuration of low floor vehicles. Furthermore, although the dynamic model, inverse model, and Smith compensator were analytically validated through MATLAB and Simulink simulations, experimental validation of the control logic has not yet been conducted due to practical constraints in the current research environment, as it requires the implementation of electrical circuits and a dedicated control microprocessor. It can be noted that the parameters of the dynamic model (Spencer model) are derived from actual measurements obtained using the rotary-type test bench, thereby enhancing the model’s reliability. This aspect is planned as future work and physical testing with the prototype RMRD for further verification of the effectiveness of the time delay compensation under real-world driving conditions.

Footnotes

ORCID iDs

Youngil Sohn

Seung-Bok Choi

Jong-Seok Oh

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This result was partially supported by the Research Program through Hyundai Motor Group (T101600223100003) and the Technology Innovation Program (RS-2024-00432266) funded by the Ministry of Trade, Industry & Energy(MOTIE, Korea).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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